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Course

PHYS-427: Relativity and cosmology I

Lectures in this course (88)

Minkowski Spacetime: Systems of Units

Introduces Minkowski spacetime, 4-vectors, physical quantities, SI units, Planck units, and HEP units.

Parallel Transport and Geodesics

Explores parallel transport along curves and geodesics maximizing proper time between points.

Exponential Map and Curvature Tensor

Covers the exponential map, covariant derivatives, connection coefficients, and Riemann curvature tensor.

Riemann Tensor and Ricci Scalar

Covers the properties of the Riemann tensor and Ricci scalar in normal coordinates.

Symmetries and Conservation Laws

Explores Killing vectors, conserved quantities, symmetric spaces, and the Riemann curvature tensor properties.

Einstein Equivalence Principle

Explores the Einstein Equivalence Principle, inertial and gravitational mass equivalence, and gravity as geometry.

Scalar Gravity: Einstein Equations

Introduces scalar gravity, covering covariant derivatives, Ricci tensor, Einstein Equivalence Principle, and the generalization of Newtonian gravity equations.

General Relativity: Einstein Equations

Introduces the Einstein-Hilbert action and discusses the generalization of gravitational field equations.

General Relativity: Energy-Momentum Tensor

Covers the Schwarzschild solution, the cosmological constant, and General Relativity as an Effective Field Theory.

Schwarzschild Metric: General Relativity

Explores the Schwarzschild metric in General Relativity, focusing on singularities and spherically symmetric solutions.

Geodesics in Schwarzschild Spacetime

Explores geodesics in Schwarzschild spacetime, circular orbits, and the perihelion advance in General Relativity.

Charged Particle in Minkowski Spacetime

Explores the worldline action of a charged particle in Minkowski spacetime, covering 4-vectors, intervals, Lorentz invariance, and charged particles in EM fields.

Gravitational Redshift & Black Holes

Explains gravitational redshift, perihelion advance, and Schwarzschild black holes.

Kruskal Coordinates: Schwarzschild Black Holes

Explores Kruskal coordinates and Schwarzschild black holes in General Relativity, including Einstein equations and cosmological constants.

Penrose Diagrams: Spacetime Visualization

Explores Penrose diagrams for visualizing black hole spacetime, emphasizing the eternal nature of black holes formed by gravitational collapse.

Astrophysical Objects: Static Systems

Explores spherically symmetric and static astrophysical objects, including black holes and the modeling of matter.

Mahler's Symphonies: Structure and Meaning

Explores Gustav Mahler's symphonies, focusing on his unique style and the conceptual depth of specific works.

Linearized Gravity: Perturbation Theory

Covers linearized gravity, perturbation theory, Einstein equations, and gravitational waves.

Gravitational Waves: Effects and Trajectories

Explores the effects of gravitational waves on geodesics and photon trajectories.

Gravitational Waves: Detection and Quadrupole Formula

Explores the production and detection of gravitational waves, the quadrupole formula, and the first observation of gravitational waves on 14/09/2015.